A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

In this paper we propose a two-stage multi-population genetic algorithm (MPGA) to solve parallel machine scheduling problems with multiple objectives. In the first stage, multiple objectives are combined via the multiplication of the relative measure of each objective. Solutions of the first stage are arranged into several sub-populations, which become the initial populations of the second stage. Each sub-population then evolves separately while an elitist strategy preserves the best individuals of each objective and the best individual of the combined objective. This approach is applied in parallel machine scheduling problems with two objectives: makespan and total weighted tardiness (TWT). The MPGA is compared with a benchmark method, the multi-objective genetic algorithm (MOGA), and shows better results for all of the objectives over a wide range of problems. The MPGA is extended to scheduling problems with three objectives: makespan, TWT, and total weighted completion times, and also performs better than MOGA.